6.78 The Los Angeles Times (June 14, 1995) reported that the U.S. Postal Service is getting speedier, with higher overnight on-time delivery rates than in the past. The Price Waterhouse accounting firm conducted an independent audit by seeding the mail with letters and recording on-time delivery rates for these letters.

Suppose that the results were as follows (these numbers are fictitious but are compatible with summary values given in the article):

Number of Letters Mailed Number of Letters Arriving on Time Los Angeles 500 425 New York 500 415 Washington, D.C. 500 405 Nationwide 6000 5220 Use the given information to estimate the following probabilities. (Hint: See Example 6.30.)

a. The probability of an on-time delivery in Los Angeles

b. The probability of late delivery in Washington, D.C.

c. The probability that two letters mailed in New York are both delivered on time

d. The probability of on-time delivery nationwide